Quark Pole Mass Research Articles

The rise and fall of the Standard-Model Higgs: electroweak vacuum stability during kination

In this paper we investigate the vacuum stability of the non-minimally coupled Standard-Model Higgs during a phase of kinetic domination following the end of inflation. The non-minimal coupling to curvature stabilises the Higgs fluctuations during inflation while driving them towards the instability scale during kination, when they can classically overcome the potential barrier separating the false electroweak vacuum from the true one at super-Planckian field values. Avoiding the instability of the Standard-Model vacuum sets an upper bound on the inflationary scale that depends both on the strength of the non-minimal interaction and on the top quark Yukawa coupling. Classical vacuum stability is guaranteed if the gravitationally-produced energy density is smaller than the height of barrier in the effective potential. Interestingly enough, thanks to the explosive particle production in the tachyonic phase, the Higgs itself can be also appointed to the role of reheaton field responsible for the onset of the hot Big Bang era, setting an additional lower bound on the inflationary scale Hinf\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{H}}_{\ extrm{inf}} $$\\end{document} ≳ 105.5 GeV. Overall, these constraints favour lower masses for the top quark, in agreement with the current measurements of the top quark pole mass. We perform our analysis semi-analytically in terms of the one-loop and three-loop running of the Standard-Model Higgs self-coupling and make use of lattice-based parametric formulas for studying the (re)heating phase derived in arXiv:2307.03774. For a specific choice of mt = 171.3 GeV we perform also an extensive numerical scanning of the parameter space via classical lattice simulations, identifying stable/unstable regions and supporting the previous analytical arguments. For this fiducial value, the heating of the Universe is achieved at temperatures in the range 10−2–109 GeV.

Relation Between Pole and Running Masses of Heavy Quarks Using the Principle of Maximum Conformality

Abstract The relation of the pole and running heavy quark masses of the order of $\mathcal {O}\left(\alpha _s^4\right)$ in perturbative quantum chromodynamics (pQCD) can be obtained using the principle of maximum conformality (PMC), a formalism that provides a rigorous method for eliminating renormalization scale and scheme ambiguities for observables in pQCD. Using PMC, optimal renormalization scale for the heavy quark mass ratio is determined, independent of the renormalization scale and scheme up to order $\alpha _s^4$. Precise values are then obtained for the PMC pole masses of the heavy quarks $M_b^{\text{PMC}}=4.86^{+0.03}_{-0.02}$ GeV, $M_t^{\text{PMC}}=172.3\pm 0.6$ GeV, and the running mass $\overline{m}_t^{\text{PMC}}=162.6\pm 0.7$ GeV at the PMC scale.

Measurement of the top quark pole mass using textrm{t}overline{textrm{t}} +jet events in the dilepton final state in proton-proton collisions at sqrt{s} = 13 TeV

A measurement of the top quark pole mass {m}_{textrm{t}}^{textrm{pole}} in events where a top quark-antiquark pair ( textrm{t}overline{textrm{t}} ) is produced in association with at least one additional jet ( textrm{t}overline{textrm{t}} +jet) is presented. This analysis is performed using proton-proton collision data at sqrt{s} = 13 TeV collected by the CMS experiment at the CERN LHC, corresponding to a total integrated luminosity of 36.3 fb−1. Events with two opposite-sign leptons in the final state (e+e−, μ+μ−, e±μ∓) are analyzed. The reconstruction of the main observable and the event classification are optimized using multivariate analysis techniques based on machine learning. The production cross section is measured as a function of the inverse of the invariant mass of the textrm{t}overline{textrm{t}} +jet system at the parton level using a maximum likelihood unfolding. Given a reference parton distribution function (PDF), the top quark pole mass is extracted using the theoretical predictions at next-to-leading order. For the ABMP16NLO PDF, this results in {m}_{textrm{t}}^{textrm{pole}} = 172.93 ± 1.36 GeV.

Recent top quark measurements with the CMS experiment

Latest results on top quark pair and single top quark production cross sections (inclusive and differential) are presented using proton-proton collision data collected by CMS. The results are used to constrain the standard model parameters. For the first time, the third row of the CKM matrix is measured from single top quark events and multidifferential cross sections are used to constrain simultaneously the top quark pole mass, α S , and PDFs. Moreover, recent results on top quark properties, such as mass measurements or constraints on top Yukawa from differential cross sections are also presented.

Pole mass renormalon and its ramifications

I review the structure of the leading infrared renormalon divergence of the relation between the pole mass and the overline{mathrm{MS}} mass of a heavy quark, with applications to the top, bottom and charm quark. That the pole quark mass definition must be abandoned in precision computations is a well-known consequence of the rapidly diverging series. The definitions and physics motivations of several leading renormalon-free, short-distance mass definitions suitable for processes involving nearly on-shell heavy quarks are discussed.

Nonintegrable threshold singularities of two-point functions in perturbation theory

In perturbation theory, the spectral densities of two-point functions develop non-integrable threshold singularities at higher orders. In QCD, such singularities emerge when calculating the diagrams in terms of the pole quark mass, and they become stronger when one rearranges the perturbative expansion in terms of the running quark mass. In this paper we discuss the proper way to handle such singularities.

NNLO compatibility between pQCD theory and phenomenology in determination of the b-quark pole and MS¯ running masses

This contribution attempts to determine the [Formula: see text]-quark pole mass [Formula: see text] and [Formula: see text] running mass [Formula: see text] with two different approaches at the next-to-next-to-leading order (NNLO) corrections. At the first approach, we derive a relation between the [Formula: see text]-quark pole mass [Formula: see text] and its [Formula: see text] running mass [Formula: see text] at the NNLO corrections based on the perturbative Quantum Chromo Dynamics (pQCD) predictions. At the second approach, we extract numerical values of the [Formula: see text]-quark pole and [Formula: see text] running masses based on the NNLO phenomenology of H1 and ZEUS Collaborations combined beauty vertex production experimental data. Then we discuss about the compatibility between the pQCD theory results and phenomenology approach in determination of the [Formula: see text]-quark pole and [Formula: see text] running masses at the NNLO corrections. Also, we investigate the role and influence of the [Formula: see text]-quark mass as an extra degree of freedom added to the input parameters of the Standard Model Lagrangian, on the improvement of the uncertainty band of the proton parton distribution functions (PDFs) and particularly on the gluon distribution.

Measurement of hbox {t}{bar{hbox {t}}} normalised multi-differential cross sections in {text {p}}{text {p}} collisions at sqrt{s}=13,{text {TeV}} , and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions

Normalised multi-differential cross sections for top quark pair (hbox {t}{bar{hbox {t}}}) production are measured in proton-proton collisions at a centre-of-mass energy of 13,{text {TeV}} using events containing two oppositely charged leptons. The analysed data were recorded with the CMS detector in 2016 and correspond to an integrated luminosity of 35.9{,{text {fb}}^{-1}} . The double-differential hbox {t}{bar{hbox {t}}} cross section is measured as a function of the kinematic properties of the top quark and of the hbox {t}{bar{hbox {t}}} system at parton level in the full phase space. A triple-differential measurement is performed as a function of the invariant mass and rapidity of the hbox {t}{bar{hbox {t}}} system and the multiplicity of additional jets at particle level. The data are compared to predictions of Monte Carlo event generators that complement next-to-leading-order (NLO) quantum chromodynamics (QCD) calculations with parton showers. Together with a fixed-order NLO QCD calculation, the triple-differential measurement is used to extract values of the strong coupling strength alpha _{S} and the top quark pole mass (m_{{text {t}}}^{{text {pole}}}) using several sets of parton distribution functions (PDFs). The measurement of m_{{text {t}}}^{{text {pole}}} exploits the sensitivity of the hbox {t}{bar{hbox {t}}} invariant mass distribution to m_{{text {t}}}^{{text {pole}}} near the production threshold. Furthermore, a simultaneous fit of the PDFs, alpha _{S}, and m_{{text {t}}}^{{text {pole}}} is performed at NLO, demonstrating that the new data have significant impact on the gluon PDF, and at the same time allow an accurate determination of alpha _{S} and m_{{text {t}}}^{{text {pole}}}. The values alpha _{S}(m_{{text {Z}}}) = 0.1135{}^{+0.0021}_{-0.0017} and m_{{text {t}}}^{{text {pole}}} = 170.5 pm 0.8 ,{text {GeV}} are extracted, which account for experimental and theoretical uncertainties, the latter being estimated from NLO scale variations. Possible effects from Coulomb and soft-gluon resummation near the hbox {t}{bar{hbox {t}}} production threshold are neglected in these parameter extractions. A rough estimate of these effects indicates an expected correction of m_{{text {t}}}^{{text {pole}}} of the order of +1 ,{text {GeV}} , which can be regarded as additional theoretical uncertainty in the current m_{{text {t}}}^{{text {pole}}} extraction.

Measurement of the tbar{t} production cross-section and lepton differential distributions in emu dilepton events from pp collisions at sqrt{s}=13,text {TeV} with the ATLAS detector

The inclusive top quark pair (tbar{t}) production cross-section sigma _{tbar{t}} has been measured in proton–proton collisions at sqrt{s}=13,text {TeV}, using 36.1 fb^{-1} of data collected in 2015–2016 by the ATLAS experiment at the LHC. Using events with an opposite-charge emu pair and b-tagged jets, the cross-section is measured to be: σtt¯=826.4±3.6(stat)±11.5(syst)±15.7(lumi)±1.9(beam)pb,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\sigma _{t\\bar{t}} = 826.4 \\pm 3.6\\,\\mathrm {(stat)}\\ \\pm 11.5\\,\\mathrm {(syst)}\\ \\pm 15.7\\,\\mathrm {(lumi)}\\ \\pm 1.9\\,\\mathrm {(beam)}\\,\\mathrm {pb}, \\end{aligned}$$\\end{document}where the uncertainties reflect the limited size of the data sample, experimental and theoretical systematic effects, the integrated luminosity, and the LHC beam energy, giving a total uncertainty of 2.4%. The result is consistent with theoretical QCD calculations at next-to-next-to-leading order. It is used to determine the top quark pole mass via the dependence of the predicted cross-section on m_t^{mathrm{pole}}, giving m_t^{mathrm{pole}}=173.1^{+2.0}_{-2.1},text {GeV}. It is also combined with measurements at sqrt{s}=7,text {TeV} and sqrt{s}=8,text {TeV} to derive ratios and double ratios of tbar{t} and Z cross-sections at different energies. The same event sample is used to measure absolute and normalised differential cross-sections as functions of single-lepton and dilepton kinematic variables, and the results are compared with predictions from various Monte Carlo event generators.

Top quark pair production near threshold: single/double distributions and mass determination

We investigate top quark pair production near the threshold where the pair invariant mass {M}_{toverline{t}} approaches 2mt, which provides sensitive observables to extract the top quark mass mt. Using the effective field theory methods, we derive a factorization and resummation formula for kinematic distributions in the threshold limit up to the next-to- leading power, which resums higher order Coulomb corrections to all orders in the strong coupling constant. Our formula is similar to those in the literature but differs in several important aspects. We apply our formula to the {M}_{toverline{t}} distribution, as well as to the double differential cross section with respect to {M}_{toverline{t}} and the rapidity of the toverline{t} pair. We find that the resummation effects significantly increase the cross sections near the threshold, and lead to predictions better compatible with experimental data than the fixed-order ones. We demonstrate that incorporating resummation effects in the top quark mass determination can shift the extracted value of mt by as large as 1.4 GeV. The shift is much larger than the estimated uncertainties in previous experimental studies, and leads to a value of the top quark pole mass more consistent with the current world average.

Hyperasymptotic approximation to the top, bottom, and charm pole mass

We construct hyperasymptotic expansions for the heavy quark pole mass regulated using the principal value (PV) prescription. We apply such hyperasymptotic expansions to the $B/D$ meson masses, and $\bar \Lambda $ computed in the lattice. The issue of the uncertainty of the (top) pole mass is critically reexamined. The present theoretical uncertainty in the relation between ${\bar m}_t$, the $\bar{\rm MS}$ top mass, and $m_{t, \rm PV}$, the top pole mass regulated using the PV prescription, is numerically assessed to be $\delta m_{t,\rm PV}= 28\;{\rm MeV}$ for ${\bar m}_t =163$ GeV.

Dependence of Five- and Six-Loop Estimated QCD Corrections to the Relation between Pole and Running Masses of Heavy Quarks on the Number of Light Flavors

In this paper various theoretical approaches are used to define the dependence of the estimated $\mathcal{O}(\alpha^5_s)$ and $\mathcal{O}(\alpha^6_s)$-corrections to the QCD relation between pole and $\rm{\overline{MS}}$ running masses of heavy quarks on the number of light flavours. It is found that recently studied asymptotic formula for the coefficients of this relation, based on the infared-renormalon method, does not reproduce sign-alternating structure in the flavour-dependence of the five and six-loop corrections, which holds in three other used by us approaches.

Scale-invariant instantons and the complete lifetime of the standard model

In a classically scale-invariant quantum field theory, tunneling rates are infrared divergent due to the existence of instantons of any size. While one expects such divergences to be resolved by quantum effects, it has been unclear how higher-loop corrections can resolve a problem appearing already at one loop. With a careful power counting, we uncover a series of loop contributions that dominate over the one-loop result and sum all the necessary terms. We also clarify previously incomplete treatments of related issues pertaining to global symmetries, gauge fixing and finite mass effects. In addition, we produce exact closed-form solutions for the functional determinants over scalars, fermions and vector bosons around the scale-invariant bounce, demonstrating manifest gauge invariance in the vector case. With these problems solved, we produce the first complete calculation of the lifetime of our universe: 10^139 years. With 95% confidence, we expect our universe to last more than 10^58 years. The uncertainty is part experimental uncertainty on the top quark mass and on ${\alpha}s$ and part theory uncertainty from electroweak threshold corrections. Using our complete result, we provide phase diagrams in the $mt/mh$ and the $mt/{\alpha}s$ planes, with uncertainty bands. To rule out absolute stability to $3{\sigma}$ confidence, the uncertainty on the top quark pole mass would have to be pushed below 250 MeV or the uncertainty on ${\alpha}s(mZ)$ pushed below 0.00025.

Erratum to: On the relation between pole and running heavy quark masses beyond the four-loop approximation

Citations in the original article are corrupted due to error made by Editors QUARKS-2018. See the Full text with correct citations in PDF file.

On the relation between pole and running heavy quark masses beyond the four-loop approximation

The effective charges motivated method is applied to the relation between pole and M̅S̅-scheme heavy quark masses to study high order perturbative QCD corrections in the observable quantities proportional to the running quark masses. The non-calculated five- and six-loop perturbative QCD coefficients are estimated. This approach predicts for these terms the sign-alternating expansion in powers of number of lighter flavors nl, while the analyzed recently infrared renormalon asymptotic expressions do not reproduce the same behavior. We emphasize that coefficients of the quark mass relation contain proportional to π2 effects, which result from analytical continuation from the Euclidean region, where the scales of the running masses and QCD coupling constant are initially fixed, to the Minkowskian region, where the pole masses and the running QCD parameters are determined. For the t-quark the asymptotic nature of the non-resummed PT mass relation does not manifest itself at six-loops, while for the b-quark the minimal PT term appears at the probed by direct calculations four-loop level. The recent infrared renormalon based studies support these conclusions.

Bottom and charm mass determinations from global fits to Qoverline{Q} bound states at N3LO

The bottomonium spectrum up to n = 3 is studied within Non-Relativistic Quantum Chromodynamics up to N3LO. We consider finite charm quark mass effects both in the QCD potential and the overline{mathrm{MS}} -pole mass relation up to third order in the Y-scheme counting. The u = 1/2 renormalon of the static potential is canceled by expressing the bottom quark pole mass in terms of the MSR mass. A careful investigation of scale variation reveals that, while n = 1, 2 states are well behaved within perturbation theory, n = 3 bound states are no longer reliable. We carry out our analysis in the nℓ = 3 and nℓ = 4 schemes and conclude that, as long as finite mc effects are smoothly incorporated in the MSR mass definition, the difference between the two schemes is rather small. Performing a fit to boverline{b} bound states we find {overline{m}}_bleft({overline{m}}_bright) = 4.216 ± 0.039 GeV. We extend our analysis to the lowest lying charmonium states finding {overline{m}}_cleft({overline{m}}_cright) = 1.273 ± 0.054 GeV. Finally, we perform simultaneous fits for {overline{m}}_b and αs finding {alpha}_s^{left({n}_f=5right)}left({m}_Zright)=0.1178pm 0.0051 . Additionally, using a modified version of the MSR mass with lighter massive quarks we are able to predict the uncalculated mathcal{O}left({alpha}_s^4right) virtual massive quark corrections to the relation between the overline{mathrm{MS}} and pole masses.

Measurement of lepton differential distributions and the top quark mass in tbar{t} production in pp collisions at sqrt{s}=8\xa0TeV with the ATLAS detector

This paper presents single lepton and dilepton kinematic distributions measured in dileptonic tbar{t} events produced in 20.2hbox {fb}^{-1} of sqrt{s}=8 TeV pp collisions recorded by the ATLAS experiment at the LHC. Both absolute and normalised differential cross-sections are measured, using events with an opposite-charge emu pair and one or two b-tagged jets. The cross-sections are measured in a fiducial region corresponding to the detector acceptance for leptons, and are compared to the predictions from a variety of Monte Carlo event generators, as well as fixed-order QCD calculations, exploring the sensitivity of the cross-sections to the gluon parton distribution function. Some of the distributions are also sensitive to the top quark pole mass; a combined fit of NLO fixed-order predictions to all the measured distributions yields a top quark mass value of {m_t^{mathrm {pole}}}=173.2pm 0.9pm 0.8pm 1.2 GeV, where the three uncertainties arise from data statistics, experimental systematics, and theoretical sources.

On the light massive flavor dependence of the large order asymptotic behavior and the ambiguity of the pole mass

We provide a systematic renormalization group formalism for the mass effects in the relation of the pole mass mQpole and short-distance masses such as the overline{mathrm{MS}} mass {overline{m}}_Q of a heavy quark Q, coming from virtual loop insertions of massive quarks lighter than Q. The formalism reflects the constraints from heavy quark symmetry and entails a combined matching and evolution procedure that allows to disentangle and successively integrate out the corrections coming from the lighter massive quarks and the momentum regions between them and to precisely control the large order asymptotic behavior. With the formalism we systematically sum logarithms of ratios of the lighter quark masses and mQ, relate the QCD corrections for different external heavy quarks to each other, predict the mathcal{O}left({alpha}_s^4right) virtual quark mass corrections in the pole- overline{mathrm{MS}} mass relation, calculate the pole mass differences for the top, bottom and charm quarks with a precision of around 20 MeV and analyze the decoupling of the lighter massive quark flavors at large orders. The summation of logarithms is most relevant for the top quark pole mass mtpole, where the hierarchy to the bottom and charm quarks is large. We determine the ambiguity of the pole mass for top, bottom and charm quarks in different scenarios with massive or massless bottom and charm quarks in a way consistent with heavy quark symmetry, and we find that it is 250 MeV. The ambiguity is larger than current projections for the precision of top quark mass measurements in the high-luminosity phase of the LHC.

Strong dynamics in a classically scale invariant extension of the standard model with a flat potential

We investigate the scenario where the standard model is extended with classical scale invariance, which is broken by chiral symmetry breaking and confinement in a new strongly coupled gauge theory that resembles QCD. The standard model Higgs field emerges as a result of the mixing of a scalar meson in the new strong dynamics and a massless elementary scalar field. The mass and scalar decay constant of that scalar meson, which are generated dynamically in the new gauge theory, give rise to the Higgs field mass term, automatically possessing the correct negative sign by the bosonic seesaw mechanism. Using analogy with QCD, we evaluate the dynamical scale of the new gauge theory and further make quantitative predictions for light pseudo-Nambu-Goldstone bosons associated with the spontaneous breaking of axial symmetry along chiral symmetry breaking in the new gauge theory. A prominent consequence of the scenario is that there should be a standard model gauge singlet pseudo-Nambu-Goldstone boson with mass below 220 GeV, which couples to two electroweak gauge bosons through the Wess-Zumino-Witten term, whose strength is thus determined by the dynamical scale of the new gauge theory. Other pseudo-Nambu-Goldstone bosons, charged under the electroweak gauge groups, also appear. Concerning the theoretical aspects, it is shown that the scalar quartic coupling can vanish at the Planck scale with the top quark pole mass as large as 172.5 GeV, realizing the flatland scenario without being in tension with the current experimental data.

Higgs-portal assisted Higgs inflation with a sizeable tensor-to-scalar ratio

We show that the Higgs portal interactions involving extra dark Higgs field can save generically the original Higgs inflation of the standard model (SM) from the problem of a deep non-SM vacuum in the SM Higgs potential. Specifically, we show that such interactions disconnect the top quark pole mass from inflationary observables and allow multi-dimensional parameter space to save the Higgs inflation, thanks to the additional parameters (the dark Higgs boson mass mϕ, the mixing angle α between the SM Higgs H and dark Higgs Φ, and the mixed quartic coupling) affecting RG-running of the Higgs quartic coupling. The effect of Higgs portal interactions may lead to a larger tensor-to-scalar ratio, 0.08 ≲ r ≲ 0.1, by adjusting relevant parameters in wide ranges of α and mϕ, some region of which can be probed at future colliders. Performing a numerical analysis we find an allowed region of parameters, matching the latest Planck data.